Stochastic Loewner evolution for conformal field theories with Lie-group symmetries

TL;DR

This paper extends Stochastic Loewner evolution to critical systems with Lie-group symmetries, linking it to the Knizhnik-Zamolodchikov equation for correlation functions in models like SU(2) Wess-Zumino-Witten.

Contribution

It introduces a novel stochastic approach for systems with continuous symmetries, connecting SLE to conformal field theories with Lie-group structures.

Findings

Stochastic evolution reproduces Knizhnik-Zamolodchikov equations.

Extension of SLE to systems with SU(2) symmetry.

Domain walls carry spin 1/2 degrees of freedom.

Abstract

The Stochastic Loewner evolution is a recent tool in the study of two-dimensional critical systems. We extend this approach to the case of critical systems with continuous symmetries, such as SU(2) Wess-Zumino-Witten models, where domain walls carry an additional spin 1/2 degree of freedom. We show that the stochastic evolution results in the Knizhnik-Zamolodchikov equation for correlation functions.